Question Number 11563 by Nayon last updated on 28/Mar/17
![if f(x)=g(y) then why (d/dx)(f(x))=(d/dy)(g(y))?](https://www.tinkutara.com/question/Q11563.png)
$${if}\:\:{f}\left({x}\right)={g}\left({y}\right) \\ $$$${then}\:{why}\:\frac{{d}}{{dx}}\left({f}\left({x}\right)\right)=\frac{{d}}{{dy}}\left({g}\left({y}\right)\right)? \\ $$
Commented by mrW1 last updated on 28/Mar/17
![this is not always correct. but (d/dx)(f(x))=(d/dy)(g(y))×(dy/dx) let′s look at x^2 =y^3 +1 (d/dx)(f(x))=2x (d/dy)(g(y))=3y^2 (d/dx)(f(x))≠(d/dy)(g(y))](https://www.tinkutara.com/question/Q11568.png)
$${this}\:{is}\:{not}\:{always}\:{correct}.\:{but} \\ $$$$\frac{{d}}{{dx}}\left({f}\left({x}\right)\right)=\frac{{d}}{{dy}}\left({g}\left({y}\right)\right)×\frac{{dy}}{{dx}} \\ $$$$ \\ $$$${let}'{s}\:{look}\:{at} \\ $$$${x}^{\mathrm{2}} ={y}^{\mathrm{3}} +\mathrm{1} \\ $$$$\frac{{d}}{{dx}}\left({f}\left({x}\right)\right)=\mathrm{2}{x} \\ $$$$\frac{{d}}{{dy}}\left({g}\left({y}\right)\right)=\mathrm{3}{y}^{\mathrm{2}} \\ $$$$\frac{{d}}{{dx}}\left({f}\left({x}\right)\right)\neq\frac{{d}}{{dy}}\left({g}\left({y}\right)\right) \\ $$
Commented by Nayon last updated on 28/Mar/17
![mrw1 please ans the question id no.11571](https://www.tinkutara.com/question/Q11572.png)
$${mrw}\mathrm{1}\:{please}\:{ans}\:{the}\:{question}\:{id}\:{no}.\mathrm{11571} \\ $$
Answered by sma3l2996 last updated on 28/Mar/17
![that not correct the correct is : if f(x)=g(y) d(f(x))=d(g(y))⇔((d(f(x)))/dx)dx=((d(g(y)))/dy)dy](https://www.tinkutara.com/question/Q11569.png)
$${that}\:{not}\:{correct} \\ $$$${the}\:{correct}\:{is}\:: \\ $$$${if}\:{f}\left({x}\right)={g}\left({y}\right) \\ $$$${d}\left({f}\left({x}\right)\right)={d}\left({g}\left({y}\right)\right)\Leftrightarrow\frac{{d}\left({f}\left({x}\right)\right)}{{dx}}{dx}=\frac{{d}\left({g}\left({y}\right)\right)}{{dy}}{dy} \\ $$